A Simple Method for Melodic Analysis and Classification¶
Sorbonne Universités / Universités Pierre et Marie Curie et Paris Sorbonne
June 10-11-12, 2015 Paris, France
Introduction : Aims and general approach¶
- To « analyse » and classify a big number of melodies
- Analysis from audio files (no symbolic data)
- A classification based on the scale proximity
- Toward an unsupervised approach (not a template-match approch)
- A simple method ?
- A Python Module : Diastema (https://github.com/AnasGhrab/diastema)
In [1]:
%matplotlib inline
from diastema import *
from IPython.display import Audio
Step 1 : Fondamental frequency (f0) detection¶
- Praat
- PitchYinFFT (Essentia)
- PredominantMelody (Essentia)
In [2]:
path = "/Users/anas/AUDIO/quatre_chants/"
Chants = Melodies(path,transpose="No",xmin=250,xmax=500,minFrequency=0,maxFrequency=700)
In [3]:
Audio(filename=path+Chants.melodies[0].file_label+".wav")
Out[3]:
In [4]:
for i in range(0,len(Chants.melodies)):
Chants.melodies[i].plot()
Step 2 : Frequency Density Estimation¶
- The main notes of the melody correspond to a high density of the frequencies. These can be represented by a Probability Density Function (PDF)
- A way to estimate PDF is using a Kernel Density Estimation (Gaussian Kernels : http://docs.scipy.org/doc/scipy-0.15.1/reference/generated/scipy.stats.gaussian_kde.html)
In [5]:
Chants.PdfsPlot(allplots="Yes",gpdf="No")
In [6]:
Chants = Melodies(path,transpose="No",xmin=250,xmax=500,minFrequency=0,maxFrequency=700,bw_method=0.15)
Chants.PdfsPlot(allplots="Yes",gpdf="No")
Step 3 : Tonic detection¶
- Extract the last frequencies (0.5%, 1%, 1.5%)
- The tonic can be :
- the most present frequency : mode()
- The most probable frequency : KDE->PDF
In [7]:
Chants.AllTonics([0.5,1,1.5,2,5,15],method="pdf")
In [8]:
Chants.AllTonics([0.5,1,1.5,2,5,15],method="mode")
Step 3bis (optional) : Getting the scale based of the detected tonic¶
In [9]:
for i in range(0,len(Chants.melodies)):
print Chants.melodies[i].get_intervals(percent=0.5,method="pdf",unit="savart")
In [10]:
for i in range(0,len(Chants.melodies)):
print Chants.melodies[i].get_intervals(percent=0.5,method="mode",unit="savart")
Step 4 : Transposition : tonic or mode ?¶
In [11]:
Chants = Melodies(path,transpose="Yes",freqref=300,xmin=250,xmax=420,bw_method=0.15)
Chants.PdfsPlot(allplots="Yes",gpdf="No")
In [12]:
Chants = Melodies(path,transpose="Yes",transpositionref="tonic",freqref=300,xmin=250,xmax=420,bw_method=0.15)
Chants.PdfsPlot(allplots="Yes",gpdf="No")
Step 4 : Correlation / Distances¶
In [41]:
data_dist = Chants.PdfCorr(out="pdist",metric='euclidean')
data_dist
Out[41]:
In [34]:
data_link = linkage(data_dist,method='complete') # computing the linkage
data_link
Out[34]:
Step 5 Hierarchical Clustering¶
In [35]:
dendrogram(data_link,labels=Chants.file_names)
plt.xlabel('Samples')
plt.ylabel('Distance')
plt.suptitle('Four melodies', fontweight='bold', fontsize=14);
Step 6 : Similarity matrix / Heatmap¶
In [36]:
# As explained here : http://nbviewer.ipython.org/github/OxanaSachenkova/hclust-python/blob/master/hclust.ipynb
# Compute and plot first dendrogram.
fig = plt.figure(figsize=(8,8))
# x ywidth height
ax1 = fig.add_axes([0.05,0.1,0.2,0.6])
Y = linkage(data_dist, method='complete')
Z1 = dendrogram(Y, orientation='right',labels=Chants.file_names) # adding/removing the axes
ax1.set_xticks([])
# Compute and plot second dendrogram.
ax2 = fig.add_axes([0.4,0.71,0.6,0.2])
Z2 = dendrogram(Y)
ax2.set_xticks([])
ax2.set_yticks([])
#Compute and plot the heatmap
axmatrix = fig.add_axes([0.4,0.1,0.6,0.6])
idx1 = Z1['leaves']
idx2 = Z2['leaves']
D = squareform(data_dist)
D = D[idx1,:]
D = D[:,idx2]
im = axmatrix.matshow(D, aspect='auto', origin='lower', cmap=plt.cm.YlGnBu)
axmatrix.set_xticks([])
axmatrix.set_yticks([])
# Plot colorbar.
axcolor = fig.add_axes([1.01,0.1,0.02,0.6])
plt.colorbar(im, cax=axcolor);
Toward a clustering of traditional woman songs in Tunisia (309 songs)¶
In [3]:
path = "/Users/anas/AUDIO/Chants_femmes/"
Chants = Melodies(path,transpose="Yes")
In [11]:
# As explained here : http://nbviewer.ipython.org/github/OxanaSachenkova/hclust-python/blob/master/hclust.ipynb
# Compute and plot first dendrogram.
fig = plt.figure(figsize=(6,100))
# x ywidth height
#ax1 = fig.add_axes([1,1,3,3])
Y = linkage(Chants.PdfCorr(),method='complete')
Z1 = dendrogram(Y, orientation='right',labels=Chants.file_names) # adding/removing the axes
ax1.set_xticks([]);
In [16]:
for i in range(0,len(Chants.melodies)):
print i, Chants.melodies[i].file_label
In [25]:
plt.figure(figsize=(16,9))
Chants.melodies[74].pdf_show() # Ghom_15
Chants.melodies[70].pdf_show() # Ghom_11
Chants.melodies[71].pdf_show() # Ghom_12
Links¶
- Diastema : Diastema (https://github.com/AnasGhrab/diastema)
- Salamon, Justin, and Emilia Gómez. “Melody Extraction from Polyphonic Music Signals Using Pitch Contour Characteristics.” Audio, Speech, and Language Processing, IEEE Transactions on 20, no. 6 (2012): 1759–70. (see also Melody Extraction : http://www.justinsalamon.com/melody-extraction.html)
- Heatmap with Python : http://nbviewer.ipython.org/github/OxanaSachenkova/hclust-python/blob/master/hclust.ipynb
- Extract Cluster Elements by Color in Python Dendrograms : http://nxn.se/post/90198924975/extract-cluster-elements-by-color-in-python
- http://docs.scipy.org/doc/scipy/reference/generated/scipy.cluster.hierarchy.linkage.html
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